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arXiv · 2607.12312

Meromorphic Group Actions and the Support Theorem for Lagrangian Fibrations

Mark Andrea de Cataldo·Yoon-Joo Kim·Christian Schnell
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Abstract

We prove several new results about Lagrangian fibrations on holomorphic symplectic complex spaces, under the assumption that the total space is K\"ahler (but possibly non-compact or singular) and that the base is a complex manifold. First, we construct a meromorphic action by a family of meromorphic groups. Second, we use this structure, together with Hodge-theoretic methods, to prove a version of Ng\^o's support theorem for Lagrangian fibrations. Along the way, we prove a freeness theorem for the cohomology of compact K\"ahler spaces equipped with a meromorphic group action.

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Mark Andrea de Cataldo, Yoon-Joo Kim, Christian Schnell. 2026-07-14. Meromorphic Group Actions and the Support Theorem for Lagrangian Fibrations. https://arxiv.org/abs/2607.12312

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